{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,7]],"date-time":"2024-03-07T20:42:40Z","timestamp":1709844160308},"reference-count":13,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":2018,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2008,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We consider a modal language for affine planes, with two sorts of formulas (for points and lines) and three modal boxes. To evaluate formulas, we regard an affine plane as a Kripke frame with two sorts (points and lines) and three modal accessibility relations, namely the point-line and line-point incidence relations and the parallelism relation between lines. We show that the modal logic of affine planes in this language is not finitely axiomatisable.<\/jats:p>","DOI":"10.2178\/jsl\/1230396757","type":"journal-article","created":{"date-parts":[[2008,12,27]],"date-time":"2008-12-27T16:52:45Z","timestamp":1230396765000},"page":"940-952","source":"Crossref","is-referenced-by-count":0,"title":["The modal logic of affine planes is not finitely axiomatisable"],"prefix":"10.1017","volume":"73","author":[{"given":"Ian","family":"Hodkinson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Altaf","family":"Hussain","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200004278_ref013","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/9.5.601"},{"key":"S0022481200004278_ref003","doi-asserted-by":"publisher","DOI":"10.3166\/jancl.12.365-397"},{"key":"S0022481200004278_ref009","unstructured":"Hussain A. , Some applications for extended modal logics, Ph.D. thesis, University of London, 2007."},{"key":"S0022481200004278_ref005","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1949-009-2"},{"key":"S0022481200004278_ref002","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/7.1.59"},{"key":"S0022481200004278_ref004","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107050884"},{"key":"S0022481200004278_ref010","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1307\/mmj\/1028999131","article-title":"On representable relation algebras","volume":"11","author":"Monk","year":"1964","journal-title":"Michigan Mathematics Journal"},{"key":"S0022481200004278_ref012","first-page":"591","volume":"60","author":"Venema","year":"1995","journal-title":"Cylindric modal logic"},{"key":"S0022481200004278_ref006","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198537793.001.0001","volume-title":"Modal logic","author":"Chagrov","year":"1997"},{"key":"S0022481200004278_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-5587-4"},{"key":"S0022481200004278_ref007","volume-title":"An introduction to the theory of numbers","author":"Hardy","year":"1979"},{"key":"S0022481200004278_ref008","volume-title":"Projective planes","author":"Hughes","year":"1973"},{"key":"S0022481200004278_ref011","volume-title":"Elementary theory of numbers","author":"Sierpi\u0144ski","year":"1964"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200004278","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,7]],"date-time":"2024-03-07T20:07:09Z","timestamp":1709842029000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200004278\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,9]]},"references-count":13,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2008,9]]}},"alternative-id":["S0022481200004278"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1230396757","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,9]]}}}